A pipeline system provided on-board an aircraft, such as, for example, the pipeline system of an aircraft air-conditioning system, normally consists of a multiplicity of individual pipeline portions, the ends of which must be connected to each other in a sealing manner when the pipeline system is being assembled in the aircraft. Sleeves composed of rubber are normally used to connect pipeline portions having a round or an oval cross-section, which sleeves are fastened by means of pipe clamps to the two ends of the pipeline portions that are to be connected to each other. The connection of two flat channel portions, by contrast, is effected by means of flange elements, which are fitted onto the two ends of the flat channel portions that are to be connected to each other, and are fixedly connected to the flat channel portions by laminating. Finally, a groove formed between an outer face of the flat channel portions and an inner face of the flange elements serves to receive a connecting element, which allows the two flat channel portions to be connected in a sealing manner. These two known arrangements for producing a connection between two pipeline portions have the disadvantage that their assembly is relatively complex, and therefore expensive.